Kinetic Theory Microstructure Modeling in Concentrated Suspensions

Emmanuelle Abisset-Chavanne,Francisco Chinesta,Amine Ammar,Rabih Mezher,Steven Le Corre

doi:10.3390/e15072805

Abstract

When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.

Highlights

Short fibers, nanofibers or carbon nanotubes—CNT—suspensions present different morphologies, depending on their concentrations
This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, solving it by using an advanced and efficient separated representation of the cluster distribution function
In the case of homogeneous flows, in absence of diffusion effects and when the initial configuration reduced to a single point, a0, in the conformational domain, Ωc, a single particle suffices for tracking the microstructure evolution, i.e., Q = 1 and

Summary

Introduction

Nanofibers or carbon nanotubes—CNT—suspensions present different morphologies, depending on their concentrations. Kinetic theory approaches [2,3,4] describe such systems at the mesoscopic scale Their main advantage is their capability to address macroscopic systems, while keeping the fine physics through a number of conformational coordinates introduced for describing the microstructure and its time evolution. At this mesoscopic scale, the microstructure is defined from a distribution function that depends on the physical space, the time and a number of conformational coordinates—the rods orientation in the case of slender body suspensions. The moments of this distribution constitute a coarser description, in general, used in macroscopic modeling [5]

Methods

Discussion

Conclusion